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The covariance is sometimes called a measure of "linear dependence" between the two random variables. That does not mean the same thing as in the context of linear algebra (see linear dependence ). When the covariance is normalized, one obtains the Pearson correlation coefficient , which gives the goodness of the fit for the best possible ...
With any number of random variables in excess of 1, the variables can be stacked into a random vector whose i th element is the i th random variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable and the j th one.
The same C(x, y) is called the autocovariance function in two instances: in time series (to denote exactly the same concept except that x and y refer to locations in time rather than in space), and in multivariate random fields (to refer to the covariance of a variable with itself, as opposed to the cross covariance between two different ...
Covariance is a measure of linear relationship between the random variables. If the relationship between the random variables is nonlinear, the covariance might not be sensitive to the relationship, which means, it does not relate the correlation between two variables. The covariance between the random variables and is [3]
The covariance matrix (also called second central moment or variance-covariance matrix) of an random vector is an matrix whose (i,j) th element is the covariance between the i th and the j th random variables. The covariance matrix is the expected value, element by element, of the matrix computed as [ []] [ []], where the superscript T ...
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
The sample mean and the sample covariance matrix are unbiased estimates of the mean and the covariance matrix of the random vector, a row vector whose j th element (j = 1, ..., K) is one of the random variables. [1] The sample covariance matrix has in the denominator rather than due to a variant of Bessel's correction: In short, the sample ...
The covariance between two complex random variables , is defined as [3] ... For a proper complex random variable, the covariance matrix of the pair ...